This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A238235 #20 Feb 17 2021 16:59:22
%S A238235 1,-1,-1,-1,1,1,-1,-17,17,31,-31,-691,691,5461,-5461,-929569,929569,
%T A238235 3202291,-3202291,-221930581,221930581,4722116521,-4722116521,
%U A238235 -968383680827,968383680827,14717667114151,-14717667114151
%N A238235 Numerators of Euler twin numbers Et(n).
%C A238235 Et(n) = 1, -1/2, -1/2, -1/4, 1/4, 1/2, -1/2, -17/8, 17/8, 31/2, -31/2, -691/4, 691/4, 5461/2, -5461/2,... =a(n)/b(n) is mentioned in A233808.
%C A238235 Denominators: b(n)= 1, 2, 2, 4, 4, 2, 2, 8, 8,... = A065176(n) with 1 instead of 0.
%C A238235 Et(n) is the first difference of 0, followed by A198631(n)/A006519(n+1).
%C A238235 Et(n+2) = -1/2, -1/4, 1/4, 1/2,... is an autosequence of the second kind. Its main diagonal is the double of the following diagonal, the inverse binomial transform of Et(n+2) being Et(n+2) signed.
%C A238235 The denominators of the difference table of Et(n+2) are even numbers of the form 2^p. For the Bernoulli twin numbers A051716(n+1)/A051717(n+2), the denominators of the difference table, A168426(n), are multiples of 3.
%F A238235 Binomial transform of A141424(n)/(A053644(n) with 1 instead of 0).
%F A238235 a(2n+3) = (-1)^n*A002425(n+2) = -a(2n+4).
%t A238235 Join[{1, -1, -1}, Table[{nu = Numerator[EulerE[2*n+1, 1]], -nu}, {n, 1, 12}]] // Flatten (* _Jean-François Alcover_, Feb 24 2014 *)
%Y A238235 Cf. A051716/A051717 (Bernoulli twin numbers).
%K A238235 sign
%O A238235 0,8
%A A238235 _Paul Curtz_, Feb 20 2014